Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
Firstly:
If someone is asked to transport some luggage and the like, this luggage is regarded as a trust under his care, and he is not liable for loss or damage unless he transgressed or was negligent, whether he is transporting it voluntarily or in return for payment. That is because in the case of one who is hired or appointed as a proxy, whatever is given to him to take care of is a trust (amanah).
It says in Sharh Muntaha al-Iradat (2/202): The proxy is in a position of trust. He is not liable if something is lost or damaged whilst in his care if he has not been negligent, because he is the proxy of the owner in possessing and disposing of it. So if it is destroyed when it is under his care, it is as if it was destroyed when under the care of its owner. This is like one who is given something for safekeeping, or the guardian of an orphan, and so on. It makes no difference whether he does that voluntarily or for payment; if he is negligent or transgresses, then he is liable. End quote.
Leaving the excess baggage in the airport is regarded as negligence, and you should have contacted the owner of the items and worked out an arrangement to transfer those goods and pay excess baggage fees, or left them with someone honest, or told her to come and get them, and the like.
Based on that, you are liable for these goods. If you can find a replacement for them, you must replace them, otherwise you are liable for their value on the day on which they were lost.
Secondly:
If there was no agreement between you regarding payment for transporting the luggage, this means that you were doing it voluntarily, and you have no right now to demand payment.
Anyone who carries luggage for someone else, or does work for him without a prior agreement on payment is doing it voluntarily, so he has no right to demand payment, unless that is his work which he does for a living, such as porters in the airport and the like. They are to be paid, even if there was no prior agreement.
It says in Kashshaf al-Qina‘ (4/206):
Whoever does work for someone else without prior agreement on fees is not entitled to anything. That is because he offered his help without stipulating anything, so he is not entitled to any payment. That is so that no one will be obliged to pay anything that he did not commit to pay. This applies if the one who offered his help was not offering to do something that he does for a living. If he does do that for a living – such as sailors, porters, cuppers, fullers, tailors, real estate agents and so on, and such as those who measure and weigh things, and the like, who earn their living by doing these things – and the owner gives him permission to do that work, then he is entitled to the same wage as his peers, because that is what is customary.
End quote.
Based on that, you are not entitled to payment, because there was no prior agreement to that effect.
You should seek reward with Allah for what happened to you, for the reward with Allah for righteous deeds will not be lost.
And Allah knows best.
